Problem: Express your answer as a mixed number simplified to lowest terms. $11\dfrac{2}{3}-9\dfrac{12}{15} = {?}$
Explanation: Simplify each fraction. $= {11\dfrac{2}{3}} - {9\dfrac{4}{5}}$ Find a common denominator for the fractions: $= {11\dfrac{10}{15}}-{9\dfrac{12}{15}}$ Convert ${11\dfrac{10}{15}}$ to ${10 + \dfrac{15}{15} + \dfrac{10}{15}}$ So the problem becomes: ${10\dfrac{25}{15}}-{9\dfrac{12}{15}}$ Separate the whole numbers from the fractional parts: $= {10} + {\dfrac{25}{15}} - {9} - {\dfrac{12}{15}}$ Bring the whole numbers together and the fractions together: $= {10} - {9} + {\dfrac{25}{15}} - {\dfrac{12}{15}}$ Subtract the whole numbers: $=1 + {\dfrac{25}{15}} - {\dfrac{12}{15}}$ Subtract the fractions: $= 1+\dfrac{13}{15}$ Combine the whole and fractional parts into a mixed number: $= 1\dfrac{13}{15}$